This coursework focuses on housing prices, with the main objective being to predict the price of a property based on various inputs. The inputs include features such as the area, the number and types of rooms, and additional factors like the availability of a main road, hot water heating, and more.
The dependent variable is the price, as it is the primary concern for most people searching for a house. The goal of this work is to predict the price based on diverse inputs, which consist of mixed data types, such as:
This project addresses a regression problem because the objective is to predict a numeric value—in this case, the price of the property.
Now we are going to import our dataset into this project.
dt_houses <- fread(file = "./Datasets/Regression_set.csv")
I would like to check, if i have some nullish data in my
dataset. I think it is a good idea to go through all rows and colums and
check, if there is a NA. I want to check it with built-in function in R
complete.cases(data_table). This function returns TRUE or FALSE
if row contains a NA value.
nas <- dt_houses[!complete.cases(dt_houses)]
nas
That looks great, now we can explore our dataset :)
Explore your data by means of select summary statistics and visualizations and present interesting findings to your reader.
Before we will explore our data, I want to import all libraries, which we will probably use:
library(data.table)
library(ggcorrplot)
library(ggExtra)
library(ggplot2)
library(ggridges)
library(ggsci)
library(ggthemes)
library(RColorBrewer)
library(svglite)
library(viridis)
library(scales)
library(rpart)
library(rpart.plot)
I found some helpful functions in R, so we could have a look on our data. We will start with a structure, than we will get some statistic data and take a head() of the data
str(dt_houses)
Classes ‘data.table’ and 'data.frame': 545 obs. of 13 variables:
$ price : int 13300000 12250000 12250000 12215000 11410000 10850000 10150000 10150000 9870000 9800000 ...
$ area : int 7420 8960 9960 7500 7420 7500 8580 16200 8100 5750 ...
$ bedrooms : int 4 4 3 4 4 3 4 5 4 3 ...
$ bathrooms : int 2 4 2 2 1 3 3 3 1 2 ...
$ stories : int 3 4 2 2 2 1 4 2 2 4 ...
$ mainroad : chr "yes" "yes" "yes" "yes" ...
$ guestroom : chr "no" "no" "no" "no" ...
$ basement : chr "no" "no" "yes" "yes" ...
$ hotwaterheating : chr "no" "no" "no" "no" ...
$ airconditioning : chr "yes" "yes" "no" "yes" ...
$ parking : int 2 3 2 3 2 2 2 0 2 1 ...
$ prefarea : chr "yes" "no" "yes" "yes" ...
$ furnishingstatus: chr "furnished" "furnished" "semi-furnished" "furnished" ...
- attr(*, ".internal.selfref")=<externalptr>
Statistic data:
summary(dt_houses[, .(price, area, bedrooms, bathrooms, stories, parking)])
price area bedrooms bathrooms stories parking
Min. : 1750000 Min. : 1650 Min. :1.000 Min. :1.000 Min. :1.000 Min. :0.0000
1st Qu.: 3430000 1st Qu.: 3600 1st Qu.:2.000 1st Qu.:1.000 1st Qu.:1.000 1st Qu.:0.0000
Median : 4340000 Median : 4600 Median :3.000 Median :1.000 Median :2.000 Median :0.0000
Mean : 4766729 Mean : 5151 Mean :2.965 Mean :1.286 Mean :1.806 Mean :0.6936
3rd Qu.: 5740000 3rd Qu.: 6360 3rd Qu.:3.000 3rd Qu.:2.000 3rd Qu.:2.000 3rd Qu.:1.0000
Max. :13300000 Max. :16200 Max. :6.000 Max. :4.000 Max. :4.000 Max. :3.0000
and this is a sample of our dataset:
head(dt_houses)
I would like to start from density of a main values, which are from my domain knowledge are important in price of the properties
We will start with price density:
ggplot(data = dt_houses, aes(x = price)) +
geom_density(fill="#f1b147", color="#f1b147", alpha=0.25) +
labs(
x = 'Price',
y = 'Density'
) +
geom_vline(xintercept = mean(dt_houses$price), linetype="dashed") +
scale_x_continuous(labels = label_number(scale = 1e-6, suffix = "M")) +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
Also it would be greate to have a look at area density:
ggplot(data = dt_houses, aes(x = area)) +
geom_density(fill="#f1b147", color="#f1b147", alpha=0.25) +
labs(
x = 'Price',
y = 'Density'
) +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
This is interesting, how does area affect price of the house. We
will plot it with points, where price is on the y-axis and area on
x-axis.
ggplot() +
geom_point(data = dt_houses, aes(x = area, y = price, color = parking)) +
scale_y_continuous(labels = label_number(scale = 1e-6, suffix = "M")) +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
This looks nice, and it is also logical, more space, higher price.
But, now I have the simplest idea, how does amount of bedrooms correlates with the price.
ggplot(data = dt_houses, aes(x = factor(bedrooms), y = price)) +
geom_boxplot() +
theme_minimal()
We can see, that on average, more bedrooms, means higher price, but I think there is not really strong relationship between this two variables.
Also it would be great to take a look at a bedrooms histogram:
ggplot(data = dt_houses, aes(x = bedrooms)) +
geom_histogram(fill="#2f9e44", color="#2f9e44", alpha=0.25) +
geom_vline(xintercept = mean(dt_houses$bedrooms), linetype="dashed") +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
Also I want to show you the mean of the bedrooms:
mean(dt_houses$bedrooms)
[1] 2.965138
Here we can see, that the most of the properties tend to have 2, 3 or 4 rooms.
Let’s also have a look at density and mean value of a stories:
ggplot(data = dt_houses, aes(x = stories)) +
geom_histogram(fill="#2f9e44", color="#2f9e44", alpha=0.25) +
geom_vline(xintercept = mean(dt_houses$stories), linetype="dashed") +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
mean(dt_houses$stories)
[1] 1.805505
It is interesting how much real estate furnished or not
ggplot(data = dt_houses, aes(x = factor(furnishingstatus), fill = factor(furnishingstatus))) +
geom_bar(color="#ced4da", alpha=0.25) +
scale_fill_viridis_d(option = "D") +
labs(title = "Bar Chart with Different Colors",
x = "Furnishing Status",
y = "Count") +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
Now, it would be great, to look at price and area distribution in differently furnished properties
ggplot(data = dt_houses, aes(y = price, x = area)) +
geom_point(data = dt_houses, aes(y = price, x = area, color = bedrooms)) +
geom_hline(yintercept = mean(dt_houses$price), linetype='dashed') +
facet_grid(.~furnishingstatus) +
scale_y_continuous(labels = label_number(scale = 1e-6, suffix = "M")) +
scale_color_distiller(type = "seq", palette = "Greens") +
theme_minimal() +
theme(axis.line = element_line(color = "#000000"))
We can also take a look on some pie charts:
dt_mainroad_counts <- as.data.frame(table(dt_houses$mainroad)) #table() - creates frequency table
colnames(dt_mainroad_counts) <- c("mainroad_status", "count")
dt_mainroad_counts$percentage <- round(dt_mainroad_counts$count / sum(dt_mainroad_counts$count) * 100, 1)
ggplot(data = dt_mainroad_counts, aes(x = "", y = count, fill = mainroad_status)) +
geom_bar(stat = "identity", width = 1, color = "white") +
coord_polar("y", start = 0) +
geom_text(aes(label = paste0(percentage, "%")),
position = position_stack(vjust = 0.5), color = "white", size = 4) +
theme_void() +
scale_fill_manual(values = c("#F1B147", "#47B1F1")) +
labs(
title = "Distribution of Mainroad Status",
fill = "Mainroad Status"
)
I think that would be enough exlporation and we can start with our first model.
Run two regression or classification models with a minimum of 5 (identical!) inputs and evaluate them in detail: Compare their performance on your data (appropriate performance metric, performance on specific regions of the input/output space) and identify potential problems/shortcomings.
If you tune a model (e.g. threshold of a logistic regression) for some metric, use only the final tuned version in the comparison with the other model.
First, I would like to start pretty simple with linear model.
I consider to take this variables in my model: area, bedrooms, bathrooms, hotwaterheating, airconditioning, stories, mainroad, parking and furnishingstatus.
I will use lm function in R to find needed beta coefficients and create my model
price_lm <- lm(formula = price ~ area + bedrooms + hotwaterheating + airconditioning + stories + mainroad + parking + furnishingstatus + bathrooms, data = dt_houses)
summary(price_lm)
Call:
lm(formula = price ~ area + bedrooms + hotwaterheating + airconditioning +
stories + mainroad + parking + furnishingstatus + bathrooms,
data = dt_houses)
Residuals:
Min 1Q Median 3Q Max
-2632747 -712077 -26462 522681 5300066
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10359.2 278618.7 0.037 0.970355
area 269.2 25.3 10.640 < 2e-16 ***
bedrooms 178658.3 76119.4 2.347 0.019285 *
hotwaterheatingyes 788761.1 236265.3 3.338 0.000901 ***
airconditioningyes 949352.9 114199.3 8.313 7.77e-16 ***
stories 373570.2 65275.8 5.723 1.75e-08 ***
mainroadyes 586360.5 149172.3 3.931 9.58e-05 ***
parking 261131.8 61971.0 4.214 2.95e-05 ***
furnishingstatussemi-furnished -91500.4 123437.7 -0.741 0.458857
furnishingstatusunfurnished -509693.4 133084.7 -3.830 0.000143 ***
bathrooms 1049426.9 108784.1 9.647 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1132000 on 534 degrees of freedom
Multiple R-squared: 0.6402, Adjusted R-squared: 0.6335
F-statistic: 95.03 on 10 and 534 DF, p-value: < 2.2e-16
We got 0.64 R-squared, which is not that bad for a model just made up. But that’s not all, I will try to do better here, but first, another model.
price_lm_mse <- mean(price_lm$residuals^2)
price_lm_mse
[1] 1.256325e+12
I think this model could perform better, because there some variables which can affect this model not only linearly, but the other way, in this case tree model can show better performance
prices_tree <- rpart(data = dt_houses, formula = price ~ area + bedrooms + hotwaterheating + airconditioning + stories + mainroad + parking + furnishingstatus + bathrooms, method = 'anova')
prp(prices_tree, digits = -3)
printcp(prices_tree)
Regression tree:
rpart(formula = price ~ area + bedrooms + hotwaterheating + airconditioning +
stories + mainroad + parking + furnishingstatus + bathrooms,
data = dt_houses, method = "anova")
Variables actually used in tree construction:
[1] airconditioning area bathrooms furnishingstatus parking
Root node error: 1.9032e+15/545 = 3.4921e+12
n= 545
CP nsplit rel error xerror xstd
1 0.304946 0 1.00000 1.00109 0.085049
2 0.094553 1 0.69505 0.71335 0.063159
3 0.053743 2 0.60050 0.61804 0.054462
4 0.026381 3 0.54676 0.58900 0.051441
5 0.024922 4 0.52038 0.58900 0.051443
6 0.022993 5 0.49546 0.58033 0.050822
7 0.021374 6 0.47246 0.55537 0.049904
8 0.015261 7 0.45109 0.54872 0.048615
9 0.012386 8 0.43583 0.52496 0.046999
10 0.010000 9 0.42344 0.52235 0.046004
prices_tree
n= 545
node), split, n, deviance, yval
* denotes terminal node
1) root 545 1.903208e+15 4766729
2) area< 5954 361 6.066751e+14 4029993
4) bathrooms< 1.5 293 3.297298e+14 3773561
8) area< 4016 174 1.437122e+14 3431227
16) furnishingstatus=unfurnished 78 4.036605e+13 2977962 *
17) furnishingstatus=furnished,semi-furnished 96 7.430067e+13 3799505 *
9) area>=4016 119 1.358098e+14 4274118 *
5) bathrooms>=1.5 68 1.746610e+14 5134912
10) airconditioning=no 44 7.024826e+13 4563682 *
11) airconditioning=yes 24 6.373358e+13 6182167 *
3) area>=5954 184 7.161564e+14 6212174
6) bathrooms< 1.5 108 2.869179e+14 5382579
12) airconditioning=no 65 1.170629e+14 4843569 *
13) airconditioning=yes 43 1.224240e+14 6197360 *
7) bathrooms>=1.5 76 2.492851e+14 7391072
14) parking< 1.5 51 7.184700e+13 6859794 *
15) parking>=1.5 25 1.336772e+14 8474878
30) airconditioning=no 10 5.146311e+13 7285600 *
31) airconditioning=yes 15 5.864106e+13 9267729 *
plotcp(prices_tree)
prices_tree_min_cp <- prices_tree$cptable[which.min(prices_tree$cptable[, "xerror"]), "CP"]
model_tree <- prune(prices_tree, cp = prices_tree_min_cp )
prp(prices_tree,digits = -3)
prices_tree_pred <- predict(prices_tree, dt_houses[, c("area","bathrooms", "bedrooms", "hotwaterheating", "airconditioning", "parking", "stories", "mainroad", "furnishingstatus")])
prices_tree_mse <- mean((dt_houses$price - prices_tree_pred)^2)
prices_tree_mse
[1] 1.478709e+12
Now I would like to upgrade my Linear model. I think that furnishing status should be treated as a factor variable, so I am going to try to upgrade my model through factor variable:
Now try to run the model with a new feature.
price_lm <- lm(formula = price ~ area + bedrooms + hotwaterheating + airconditioning + stories + mainroad + parking + furnishingstatus_factor + bathrooms, data = dt_houses)
summary(price_lm)
Call:
lm(formula = price ~ area + bedrooms + hotwaterheating + airconditioning +
stories + mainroad + parking + furnishingstatus_factor +
bathrooms, data = dt_houses)
Residuals:
Min 1Q Median 3Q Max
-2632747 -712077 -26462 522681 5300066
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 10359.2 278618.7 0.037 0.970355
area 269.2 25.3 10.640 < 2e-16 ***
bedrooms 178658.3 76119.4 2.347 0.019285 *
hotwaterheatingyes 788761.1 236265.3 3.338 0.000901 ***
airconditioningyes 949352.9 114199.3 8.313 7.77e-16 ***
stories 373570.2 65275.8 5.723 1.75e-08 ***
mainroadyes 586360.5 149172.3 3.931 9.58e-05 ***
parking 261131.8 61971.0 4.214 2.95e-05 ***
furnishingstatus_factorsemi-furnished -91500.4 123437.7 -0.741 0.458857
furnishingstatus_factorunfurnished -509693.4 133084.7 -3.830 0.000143 ***
bathrooms 1049426.9 108784.1 9.647 < 2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1132000 on 534 degrees of freedom
Multiple R-squared: 0.6402, Adjusted R-squared: 0.6335
F-statistic: 95.03 on 10 and 534 DF, p-value: < 2.2e-16
Engineer a minimum of two new features based on your data exploration or on theoretical considerations. Add these features to your models and reevaluate their performance on the same performance metrics as before.